It is conventional and well-known, for example in plants in the drinks industry, to sterilize the closures used to close filled bottles or other containers, in particular cap-like closures such as screw closures, flat caps, crown corks etc., before use, i.e. before application to the container concerned, inter alia using sterilizing agents that consist of H2O2 vapor (vaporized aqueous hydrogen peroxide solution with sufficiently high concentration of H2O2) or a gaseous and/or vaporous carrier medium enriched with H2O2 vapor. To achieve an effective sterilization with high disinfection rate, before exposure to the sterilizing agent the closures are preheated for example to a temperature in the range between 50° C. and 85° C., and then after treatment or exposure to the gaseous and/or vaporous sterilizing agent, dried using a preferably heated sterile gaseous and/or vaporous medium, for example using preferably heated sterile air, so that the sterilized closures can then be used for closing containers or supplied to a closing machine for this.